# 27 · 2^{8342438} - 1

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

#### This prime's information:

Description: | 27 · 2^{8342438} - 1 |
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Verification status (*): | Proven |

Official Comment (*): | [none] |

Unofficial Comments: | This prime has 1 user comment below. |

Proof-code(s): (*): | L3483 : Farrow, PSieve, Srsieve, PrimeGrid, LLR |

Decimal Digits: | 2511326 (log_{10} is 2511325.5063308) |

Rank (*): | 125 (digit rank is 1) |

Entrance Rank (*): | 77 |

Currently on list? (*): | short |

Submitted: | 2/1/2021 09:48:22 CDT |

Last modified: | 2/2/2021 14:50:10 CDT |

Database id: | 131654 |

Status Flags: | TrialDiv |

Score (*): | 49.4564 (normalized score 124.4655) |

#### User comments about this prime (disclaimer):

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#### Verification data:

The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions. We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.

field value prime_id 131654 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prime notes Command: /home/caldwell/clientpool/1/pfgw64 -tp -q"27*2^8342438-1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 27*2^8342438-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 5, base 1+sqrt(5) Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate Iteration: 22/8342444 ERROR: ROUND OFF 0.5>0.45 (Test aborted, try again using the -a1 switch) Running N+1 test using discriminant 5, base 1+sqrt(5) Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate Iteration: 22/8342444 ERROR: ROUND OFF 0.5>0.45 (Test aborted, try again using the -a2 (or possibly -a0) switch) Running N+1 test using discriminant 5, base 1+sqrt(5) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 27*2^8342438-1 is prime! (104175.7482s+0.0043s) [Elapsed time: 28.94 hours] modified 2021-04-20 17:39:25 created 2021-02-01 09:51:01 id 177351

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.

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